Only one smoker and one business have been taken to court for flouting Scotland's strict anti-smoking laws in the year since they were introduced, it emerged yesterday.

Critics of the ban predicted open disobedience by smokers, but Scottish ministers claimed yesterday it had been a "tremendous" success after learning that only 175 people were fined for breaching the law.

The first smoker to be prosecuted for refusing to stop smoking in an enclosed public place is due in court in Aberdeenshire next month.

More than 45,000 smokers tried to quit using NHS cessation projects last year, although only 18% succeeded in stopping long term, while air pollution surveys found that air quality rates in bars had improved by 86%.

The figures were released as the public health minister for England, Caroline Flint, visited a smoking cessation clinic in Glasgow yesterday to mark the ban's first anniversary. She said the measure "has shown us that smoke-free legislation can work. Everyone is protected from the harm of second-hand smoke when working, socialising and relaxing and it also provides a more supportive environment for smokers who wish to give up."

Ministers in London, Cardiff and Belfast are bracing themselves for defiant protests by smokers once similar prohibitions on smoking in public places are phased in across the rest of the UK over the next 100 days, with the final ban due to be in place in England in July.

Official statistics confirmed yesterday a very high rate of compliance by businesses with the regulations, which require all covered public places, including shops, cafes, taxis and factories, to display no-smoking signs. More than 55,000 workplaces had been visited but only one had been prosecuted. Another 14 had been given on-the-spot fines.

Andy Kerr, the Scottish health minister, said the public had embraced the legislation far more than expected. "I think we're further ahead than we ever thought we would be. Just weeks after the ban had been in place people had taken to it, understood it, and understood the good reasons for it.

"None of the doom and gloom occurred. None of the mass civil disobedience that was projected by some people actually happened."

Although the Scottish Licensed Trade Association said a third of bars had laid off staff after the ban and that drink takings were down 11%, opinion surveys suggest 80% of Scots believed the ban had been a success.

Pressure is now growing for further measures, with proposals due later this year to raise the legal age for buying tobacco products from 16 to 18.

The government's health advisers are considering calling for a ban on the public display of cigarettes in shops and supermarkets, forcing retailers to hide packets under the counter and to show simply a price list, although ministers are understood to favour waiting to see how successful the public smoking bans prove.

Glasgow city council, which employs 35,000 people, is expected to announce plans this week to ban its staff from smoking outside its offices, depots and schools, tearing down outdoor "smoking shelters", while doctors at a specialist cancer treatment centre in the city are to ban smoking entirely on its premises.

The British Medical Association said pregnant women who smoke should now be specially targeted, while even tougher sanctions should be used against shops which sell cigarettes to children under 16 to combat smoking among the young.

Peter Terry, who chairs BMA Scotland, said the ban had made a "huge difference" to public health, but added: "Much more needs to be done to reduce the number of smokers in Scotland, particularly among the young and pregnant women."